JOHANNESBURG—Investors and CEOs rallied around the African National Congress’s new party chief Tuesday, but the union-leader-turned-tycoon will have to balance pressures to reduce South Africa’s debt and boost growth with his own party’s demands for policies directly supporting the poor, black majority.

Cyril Ramaphosa, the deputy president and one of the country’s richest black men, campaigned on the promise of a “New Deal” for the stuttering economy and corruption-plagued government. In a party vote on Monday he beat a...